Flat-Top Polygonal Temperature Profiles by Laser Beams
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Y.F. LU Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511.
ABSTRACT A method was proposed to generate flat-top polygonal temperature distributions in substrates from a Gaussian-shaped laser source. The original Gaussian beam is equally and diametrically separated into several portions and is then rearranged so that the each portion has its peak intensity allocated toward outside. This can be realized by a symmetrical multifacet prism. A mathematical model was derived to calculate the temperature rise induced the rearranged portions of the laser beam. Flat-top polygonal temperature profiles with two, three, four and six corners have been investigated by numerical calculations. It is shown that flat-top polygonal temperature distributions can be obtained by this method if the distance between the peaks of the beam portions is arranged to be certain proportions to the original Gaussian beam. It is also found the shape of the temperature profile is almost with the same size as the original Gaussian beam size and does not depend on the incident laser power and the substrate material.
INTRODUCTION Laser material processing is a wide research field in recent years and has included several areas of laser science, laser engineering, surface analysis and material analysis.[1] In order to achieve better understanding of the processing mechanism, laser induced temperature rise becomes an important research topic because it plays a very important role in the laser-induced physical and chemical processes. The modeling of temperature distributions induced by laser radiation in solids was previously investigated by several groups such as
Lax[2,3] for stationary beams, Clime and Anthony[4] for moving beams and others[5-81. For many continuous wave (CW) lasers, their intensity profiles of the output beams have a Gaussian distribution. Consequently, the patterns generated in laser processing such as etching and deposition also have a Gaussian profile. In many applications (such as etching and lithograph in VLSI), circular patters are not suitable. Therefore, it is necessary to find how to generate fiat patterns in substrate by the Gaussian-shaped laser sources. Some efforts have been done to convert Gaussian laser beam to fiat-top intensity distribution[9,10]. In this article, we propose a method of converting a Gaussian beam to equally and diametrically separated portions located at corners of a polygon by appropriate optics (e.g., multi-facet prism). We use computer simulation to show that polygonal temperature profiles with flat tops can be generated by this mcthod. From these results, we can expect to process flat-top polygonal patterns by Gaussian laser in laser processing, especially in those heat driven laser-induced chemical reactions.
669 Mat. Res. Soc. Symp. Proc. Vol. 354 0 1995 Materials Research Society
THEORETICAL CONSIDERATIONS Assume that the geometry of the physical modeling is set in an X-Y-Z coordinate. If the thermal properties of the substrate con
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